On total labelings of graphs with prescribed weights
Muhammad Irfan, Andrea Semaničová–Feňovčíková · AKCE International Journal of Graphs and Combinatorics · 2016
Let be a finite, simple and undirected graph. The edge-magic total or vertex-magic total labeling of is a bijection from onto the set of consecutive integers , such that all the edge weights or vertex weights are equal to a constant, respectively. When all the edge weights or vertex weights are different then the labeling is called edge-antimagic or vertex-antimagic total, respectively.In this paper we provide some classes of graphs that are simultaneously super edge-magic total and super vertex-antimagic total, that is, graphs admitting labeling that has both properties at the same time. We show several results for fans, sun graphs, caterpillars and prisms.